Winning Score?

The most interesting SFTC afternoon matchup is the golf choice:

PGA Travelers (Cromwell, CT): What will be the TOURNEY-WINNING SCORE?

93% are choosing "20 under par or better." Statistical analysis indicates, however, far greater likelihood of "19 under par or worse."

The leaderboard looks like this:

Goydos 194 (-16)
Perry 195 (-15)
Toms 196 (-14)
Two tied at 197 (-13)
3 tied at 198 (-12)
3 tied at 199 (-11)

For the winner to be 20 under par or better, Goydos needs -4 (66), Perry -5 (65), etc...

How likely is that?

Through yesterday, 240 rounds were played by those who made the weekend cut. This is the distribution:

61	1	|	62	0	|	63	4	|	64	6
65	19	|	66	36	|	67	43	|	68	46
69	24	|	70	32	|	71	11	|	72	7
73	6	|	74	1	|	76	1	|	78	1

If we leave out the scores of the 8 golfers cut after yesterday's round, this is the distribution and the percentages:

score	#	percent	|	score	#	percent
61	1	0.5%	|	62	0	0.0%
63	4	1.9%	|	64	6	2.8%
65	19	8.8%	|	66	33	15.3%
67	41	19.0%	|	68	43	19.9%
69	20	9.3%	|	70	29	13.4%
71	10	4.6%	|	72	7	3.2%
73	3	1.4%

The overall mean is 67.7 with a standard deviation of 2.14. Below is the actual distribution of round scores (blue) for those who made the final cut, as well as a normalized statistical distribution (red):

Based on the normalized function, Goydos has a 21% of scoring 66 or better, Perry a 10.3% chance of scoring 65 or better, and Toms a 4.2% of scoring 64 or better.

The chances of scoring a 63 or better is 1.4%, 62 or better 0.4%, and 61 or better 0.4%.

If we put them all together, there is only a 35.6% of someone shooting 20 or under for the tournament.

With typically tougher pin placements on the final day, that number drops still further.

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Now it may be that the leaders have better than average chance of shooting the necessary low scores. That might be the case (marginally) for Perry and Tom, but probably not for Goydos. If anything, a more likely distribution for him would include the scores of those who did not make the cut, as he has missed the cut this year more often than he has made it.

All told, this pick has almost a 2:1 likelihood of panning out, far better than the great majority of SftC picks, and certainly far better than any other afternoon offerings.